The present invention relates to a holographic imaging display which is used to image a wave front of a three-dimensional scene (3D scene), said wave front being encoded on a phase modulator, into a visibility region in an observer plane, where its reconstruction can be seen from an eye position.
The invention also relates to a method which allows the wave front of the 3D scene to be encoded by way of phase encoding and then to be reconstructed in the holographic imaging display. The method also includes an iterative improvement of the control values for encoding.
The reconstruction quality of a 3D scene in a holographic display device is affected by a number of factors. Reconstruction errors are caused for example by the effects of disturbing light of other diffraction orders, which is why those diffraction orders must be suppressed. Other errors in the reconstruction are caused by the encoding method which is used, in combination with the components used, e.g. an amplitude-modulating or a phase-modulating spatial light modulator.
The thus far unpublished patent application DE 10 2006 003 741 filed by the applicant describes a method of encoding a computer-generated hologram (CGH) of a three-dimensional object based on the phase encoding principle, and a holographic display device used to implement that method. The method is based on the principle that a complex-valued reference wave front of the three-dimensional object, which is computed and summed up in the visibility region for example from transformations of section planes of the 3D scene or by another equivalent method executed in the visibility region, is stored in a processor with for example electronic means.
Object data sets contain complex phase and amplitude values of a multitude of object points in the individual object planes and thus the entire object information of the three-dimensional object. The complex-valued hologram data, which are computed from the object data sets, encode a spatial light modulator (SLM), which is capable of influencing by electronic control the amplitude and phase of light which is able to interfere. The three-dimensional object can thus be fully reconstructed from those data. The reconstruction can be seen from a visibility region if at least one eye of an observer is situated there. The three-dimensional object can either be a still object or a sequence of moving images (3D scene) of a real or virtual representation. In earlier documents filed by the applicant, this visibility region was compared with an observer window, and it also used to be referred to as such. As far as the present invention is different to the patent application mentioned above, this will be explained in more detail in the description.
Document DE 10 2006 003 741 relates to a method which is used to improve the process of encoding a CGH by way of two-phase encoding in a phase modulator. That method is described with the help of a holographic display device where an optical transformation of the wave front—which corresponds e.g. with a Fresnel transformation or with a Fourier transformation—takes place from the phase modulator into the visibility region. However, the holographic display device lacks adequate means to image the wave front from the phase modulator into the visibility region with a subsequent reconstruction of the wave front. The phase modulator contains encoded phase values, while the computed wave front in the visibility region is not merely a phase function, but comprises changing absolute values. However, in order to realise a imaging despite this, optical means must be added and/or existing ones must be modified accordingly.
A phase modulator, or phase-modulating SLM, is an electronic medium which serves to control the phase of a wave front by way of modulating an illuminating wave front emitted by one or multiple independent light sources. It consists of a multitude of electronically controllable pixels which are arranged in a regular pattern, in which a wave front or a CGH of the 3D scene is encoded. The reconstruction of the 3D scene is generated by diffraction of sufficiently coherent light at the controllable pixels.
When using a phase-modulating SLM, greater brightness of the reconstruction can be achieved compared for example with an amplitude-modulating SLM, because the pixels exhibit maximum transmittance. Another advantage of phase encoding is better wavelength dependence, because the object is reconstructed in the zeroth diffraction order of the used light, so that colour holograms can be represented better.
The method of phase encoding is generally based on the principle that a complex value can be represented by at least two phase values as complex numbers with the absolute value 1 for the amplitude. These phase values are encoded in adjacent pixels of the SLM. For example, a complex value with the phase ψ and the amplitude a ranging between 0 and 1 is thus written according to the two-phase-encoding method as phase 1=ψ+a cos a and phase 2=ψ−a cos a.
Phase encoding can be realised with k phase values each in adjacent pixels of the phase modulator, where these adjacent pixels can lie below one another and/or side by side. This is why it can generally be referred to as a phase encoding with k components.
However, it is generally also thinkable to express a number of complex values in any other way by two or more phase values per complex value. While the two-phase encoding method is used as an example in the description below, the explanations given typically also apply to a more general encoding with k phase values.
If it was possible to encode multiple phase values at one and the same position on the SLM in order to represent phase values, a thus encoded CGH would make it achievable to reconstruct the 3D scene free of errors. In practice, however, the phase values can only be written to two horizontally and/or vertically adjacent controllable pixels of the phase-modulating SLM, so that they exhibit a local offset. That offset causes errors in the reconstruction of the 3D scene. This is why measures to improve the reconstruction quality are necessary so that one can benefit from the advantages of the two-phase encoding method. This can be achieved by employing an iteration method in the CGH encoding process.
Generally, various iteration methods have been described in the literature. The best-known one is the iterative Fourier transformation algorithm according to Gerchberg and Saxton, which has been described in numerous publications, and which forms the general basis for most iteration methods. According to that method, a transformation and a back-transformation are performed repeatedly between a given function and its Fourier transform, and the deviation from the set-point values are minimised in each step in the two functions by taking advantage of degrees of freedom. The transformations are performed for example between the plane of a light modulator and the reconstruction plane of a two-dimensional object. Often the intensity distribution in the object plane is intended to reach a certain value in the reconstruction while the phases of the complex values can be chosen freely and are adapted in order to reduce the error. A complete elimination of the reconstruction errors of 3D scenes cannot be achieved this way though.
An iteration method for a hologram of a three-dimensional object has become known in the document “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping” by Gavin Sinclair et al. The object is sliced into multiple object planes. The complex actual values of the encoded hologram are transformed one after another into each of the individual object planes. In each of those planes the complex actual values are compared with the complex set-point values, and the absolute value of the actual values is replaced with the absolute value of the set-point values. The values which are back-transformed into the hologram plane are then summed up for encoding. Due to the large number of object planes and the many transformations between the individual object planes and the hologram plane, the computational load increases greatly.
In addition to the high computational load, the known methods also exhibit the disadvantage that for their use in a holographic display device certain conditions must be fulfilled precisely, which is not always feasible in practice. This is why a complete elimination of all above-mentioned influences which cause reconstruction errors is very difficult. There will always be a significant remaining error, so that high-quality reconstructions cannot be realised in holographic display devices without applying a correction method.